Nonlinear inductance



Sept. 14, 1943. H E 2,329,537

NONLINEAR INDUCTANCE Filed July 3, 1941,

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Patented Sept. 14, 1943 NONLINEAR INDUCTANCE Henry M. Huge, Lorain, Ohio, assignor or oneljialf to Closman P. Stucker and one-half to E. M. Heavens Application July 3, 1941, Serial No. 401,048 zo'ciaims. (Cl. 172-281) My invention relates to non-linear inductances and in particular to a new type of non-linear inductance to eliminate wave-shape distortion.

It is an object of my invention to produce a non-linear inductance for use in circuits where non-linear characteristics are desired but distortion is objectionable.

Another object of my invention is the provision of a saturable inductance which when energized by a sinusoidal voltage produces a current wave containing no harmonics higher than the third.

It is another object of my invention to produce a saturable inductance which when energized by a sinusoidal voltage and a constant magnetic bias produces a current wave containing no harmonics higher than the second. v

A further object of my invention is the provision of a saturable inductance which when energized by a constant magnetic bias and a sinusoidal voltage produces a current wave containing the fundamental and second harmonic only.

Another object of my invention is the provision of a saturable inductance element which when energized by a sinusoidal voltage produces a current wave containing the fundamental and the third harmonic only.

Another object of my invention is to produce a circuit which has non-linear characteristics but which does not have a tendency to distort a sinusoidal wave impressed upon it.

It is another object of my invention to produce a non-linear circuit in which the harmonics can be eliminated with a single tuned circuit.

Another object of my invention is to utilize the non-linear characteristics of a saturabie inductance without causing distortion of the voltage wave-shape across it.

A further object of my invention is to combine the non-linear characteristics of a plurality of saturable magnetic flux paths to obtain a resultant characteristic which can be expressed substantially by a cubic equation.

A still further object of my invention is to make a non-linear inductance which when used as a modulating element produces modulation of a single order.

Another object of my invention is to eliminate the frequency spectrum appearing in a non-linear inductance as a result of modulation by removing the frequency of the lowest order in the spectrum.

Another object 01' my invention is to produce a non-linear parallel combination which becomes anti-resonant under a specified applied voltage, and which passes a substantially sinusoidal current when impressed with a substantially sinusoidal voltage.

Another object of my invention is to make a non-linear inductive modulator for producing third order modulationto the substantial exclusion of modulation of all other orders.

It is another object of my invention to com bine the non-linear characteristic of a plurality of saturable magnetic flux paths to obtain a resultant characteristic which, for positive values of flux, can be expressed substantially by a quadratic equation.

Another object of my invention is to make a non-linear inductive modulator for producing a second order modulation to the substantial exclusion of modulation of all other orders.

Another object of my invention is to produce a non-linear inductance whose action in any circuit can be accurately expressed mathematically.

Other objects and a fuller understanding of my invention may be had by referring to the following description and claims, taken in conjunction with the accompanying drawing, in which:

Figure 1 shows an arrangement for combining the characteristics of a plurality of saturable magnetic flux paths consisting of connecting the exciting winding of these flux paths in series;

Figure 2 shows an arrangement for obtaining results comparable with those of Figure 1 in a single core construction;

Figure '3 shows a circuit arrangement for bypassing the harmonic current generated in a nonlinear inductance embodying the ieatures of my invention, and

Figure 4 shows a typical biasing circuit which may be connected to my non-linear inductance.

It is well known to those skilled in the art that the use of a non-linear inductance in an alternating current circuit always has been accompanied by a distortion in wave form. This phenomenon is more noticeable at the higher flux densities and at high values of saturation. In general, the more highly saturated a non-linear inductance becomes, the more harmonics it gencrates. In the past, when the harmonics were ob- Jectionable, they were eliminated by the use of elaborate filter systems because there was no other way of utilizing the non-linear properties of a saturable inductance and eliminating the undesirable harmonics generated.

I have invented a non-linear inductance in which the magnetization curve is altered to suppress the generation of higher harmonics when the inductance is energized by a sinusoidal input voltage of the supply frequency. In one embodiment of my invention the current produced by a sinusoidal exciting voltage consists only of the fundamental and third harmonic and, in a second embodiment of my invention which requires a magnetic bias on the core, the current produced by the sinusoidal exciting voltage consists only of the fundamental and second harmonic.

These two embodiments of my invention comprise, respectively, a third order and a second order modulator. In either of these embodiments of my invention, the higher harmonics can be generated by those below them in the frequency spectrum, appearing in the impressed voltage. The generation of the higher harmonics is brought about by the modulation effect. For example, if voltages of the third harmonic and fundamental are impressed upon a third order modulator made according to my invention, the modulation products will give rise to a frequency spectrum which comprises the fifth, seventh and ninth harmonics. It follows that when voltages of the fundamental, third, fifth, seventh and ninth harmonics are impressed upon the inductance they cause additional modulation, and in turn produce an additional spectrum of higher harmonics. In actual operation, the effect of modulation is as followsif a source of sinusoidal voltage supplies current through a series of impedance to a non-linear inductance of the third order modulator type made according to my invention, the flow of third harmonic current through the series impedance causes a third harmonic voltage to appear across my inductance, which in turn causes the higher harmonics to appear in the current, and consequently, in the voltage. As a result, there appears in the voltage a complete spectrum of harmonics which depend upon the presence of voltage of the frequency of the lowest order in the spectrum.

My invention goes further and contemplates the use of a low impedance path to eliminate the frequency of the lowest order in the spectrum and thereby substantially eliminate all harmonics.

By my invention, I am able to utilize the properties of a non-linear inductance and maintain a substantially sinusoidal voltage across the nonlinear inductance when the voltage supplied is sinusoidal, even though there is an impedance in series with the source of voltage.

This is possible because my inductance has the following characteristic-with a sinusoidal applied voltage only one harmonic appears in the current. Therefore, if a low impedance path is provided for this harmonic a sinusoidal voltage can readily be maintained without making any provision for the flow of current from the higher harmonics. This is particularly desirable where the non-linear characteristic is to be used in a static type voltage regulator. In this case, an unbiased core is ordinarily used and the harmonic which would be by-passed is the third harmonic.

Other devices making use of non-linear characteristics are frequency changers, magnetic amplifiers, and magnetic modulators. My invention can be used to advantage in all of these devices. Basically, the advantage of my nonlinear inductance in all these applications arises from the fact that I have restricted the modulation produced by the non-linear inductance to that of a single order. With prior non-linear inductances, the modulation which occurs when the core is biased is of the second, the third, the fourth, and higher orders, and when the core is not biased. it is of the third, the fifth, the seventh and higher orders, the relative importance of these orders of modulation depending upon the degree of saturation of the core. when using these prior non-linear inductances, it is, therefore, practically impossible to predict what the exact effects of the non-linearity in the circuit will be, and consequently, the non-linear characteristics cannot be used to the greatest advantage. By eliminating these higher orders of modulation, the uncontrolled frequencies present in the circuit are substantially eliminated and the energy which would otherwise be diverted to these higher frequencies will appear as useful energy in the output.

In the following I shall first explain how I alter the magnetization curve in order to suppress the higher harmonics in an unbiased inductance and then explain how I alter the magnetization curve to suppress the higher harmonics in a biased inductance.

In general, the relationship between the exciting current and the flux can be approximated conveniently by a series of the form:

where, i, is the instantaneous value of the exciting current, is the instantaneous value of the flux, and A1, A3, A5 and A are constants depending on the physical and electrical proportions of the inductance. To express the characteristic of any ordinary saturable inductance to a reasonable degree of approximation by this equation requires the use of at least three and usually more terms on the right hand side of the equation, so that in a mathematical analysis of an alternating current circuit including an ordinary saturable inductance the difliculties involved in obtaining a good approximation are almost insurmountable.

According to my invention I overcome these difllculties and at the same time produce a saturable inductance whose characteristics can be used to greatest advantage. I accomplish this by combining the characteristics of several saturable magnetic flux paths, so that the resultant characteristic has substantially a cubic form; that is, to a high degree of approximation it is described by the first two terms of the right hand side of the equation given above, with the other higher terms deleted.

There are several methods of combining the characteristics of the saturable flux paths, one is to connect in series with each other a number of individual inductances of varying characteristic as shown in Figure l, producing a total inductance with the desired characteristic. The individual inductances, 20, 2|, 22 and 23 may be constructed with varying numbers of turns or with different cores so that each becomes saturated at a diflerent value of current. In this manner, it is possible to obtain a combination of inductances which has substantially a cubic characteristic.

In like manner it is also possible to obtain a combination of ,inductances which has a substantially quadratic characteristic for positive values of flux. To take advantage of this quadratic characteristic it is necessary to provide an unidirectional bias of sufllcient magnitude to prevent flux reversals.

Many methods of biasing cores are known to those skilled in the art and Figure 4 shows a typical biasing circuit. Terminals 20 and II on the biasing arrangement may be connected to terminals ll and 10 on the inductance made in ferent saturation characteristics.

accordance with my invention. In Figure 4 resistance 26 is used to adjust the magnitude of the biasing current supplied by battery 28, and inductance 21 is used to prevent the flow of alternating current through the battery 28.

I prefer, however, to make use of a core construction such as is shown in Figure 2 to obtain with a single inductance element the equivalent of a number of series-connected inductances.

In my invention, the laminated core may be divided into a plurality of sections, and in Figure 2 I have illustrated, for example, four such sections, designated H, l2, l3 and I4. Winding 10, having terminals l8 and i9, is common to all the core sections so they all have the same impressed magneto-motive force. The core sections are arranged to saturate under difierent magneto-motive forces by introducing non-magnetic material in their magnetic paths, or by using sections of magnetic core material having dif- For example, section Ii may have a non-magnetic gap iii of .010 inches between the E and I sections, section l2 a gap I6 of .005 inch, section l3 9. gap ll of .002 inch and section l4 may be made with a substantially closed magnetic path by interleaving the individual laminations.

In the core of Figure 2, the sections of the core constitute parallel flux paths, the total flux linking with the winding I being the sum of the fluxes in the individual sections. The section l4 saturates at a relatively low magnetizing force, section l3 at a higher magnetizing force, section l2 at a still higher magnetizing force, and section II require-the greatest magnetizing force. Section l4 saturates at a low magnetizing force and thereafter the flux in this section increases very little but inasmuch as section [3 is still unsaturated, the flux through it increases at a great enough rate to maintain the desired shape of the characteristic curve. After section i3 becomes saturated, section I! supplies the increase in flux and finally section II is effective after section I? saturates.

After section II has become highly saturated, the characteristic no longer follows the same curve, but over a very large range of operating values, the total flux and the magnetizing current can be expressed by a simple equation. If the core is to be used without bias, I prefer to construct the core to conform with an equation of the form:

If the core is to be biased I preferto construct it to conform with an equation of the form:

i=Aie-i-Az b where the plus sign applies to positive value of b and the minus sign applies to negative values of It is possible to construct the core so that over most of the operating range the first power term is negligible in comparison with the higher power term. In most applications it is desirable to have the first power term as small as possible. To achieve this result, I preferably construct the core with more than four sections, or with special alloy core material in at least one of the sections, or the combination of both arrangements.

From the cubic characteristic:

i=A1+A3 it-is possible to calculate the performance of monic appears in the current.

the non-linear inductance energized wtih an alternating current source. It can be shown that when the applied voltage is sinusoidal the current will contain no harmonics other than the third and that the magnitude of the fundamental component of the current can be expressed as a function of the applied voltage in an equation of the form:

where In is the fundamental current, E the applied voltage, and B1 and B3 are constants depending upon A1 and A3.

Similarly, from the quadratic equation:

it is possible to calculate the performance of this non-linear inductance energized with an alternating current source and with a superimposed constant flux great enough to keep positive at all times. It can be shown that when the applied voltage is sinusoidal the current will contain no harmonics other than the second. This inductance acts as a second order modulator.

If a non-linear inductance made accordance to my invention is used as a modulating element;

' that is, if there are simultaneously impressed on it voltages of two different frequencies, the modulation which occurs is of the second or third order only, and the magnitudes and phases of the currents which are the modulation products can be accurately calculated.

The applications in which this type of an inductance can be used are many and varied. One type of application arises from the fact that with a sinusoidal impressed voltage only one har- This characteristic can be used to eliminate distortion in many applications, by by-passing the second or third harmonic current around any impedance in series with the non-linear inductance, as shown in Figure 3, thereby maintaining the voltage across my inductance substantially sinusoidal in shape.

The circuit of Figure 3 comprises a saturable inductance such as shown in Figure 2 shunted by a linear inductance 24 in series with a capacitor 25. The circuit of Figure 3 is adapted to be energized by an alternating voltage of a specifled frequency. The linear inductance 24 and the capacitor 25 comprise a series resonant circuit tuned to the harmonic of the supply frequency which is to be by-passed. When the saturable inductance is biasedand constructed to produce the second harmonic only, thiscircuit is tuned to the second harmonic, or when the saturable inductance is unbiased and constructed to produce the third harmonic, this circuit is tuned to the third harmonic. In Figure 3 the core of the saturable inductance may be biased by any of the well known methods. One method is to use a circuit arrangement as shown in Figure 4 and connect terminals 29 and 30 of Figure 4 to terminals I8 and H of Figure 3.

The circuit of Figure 3 is unique in that it exhibits a non-linear relationship between the voltage applied on terminals l8 and 19, yet it does not produce a wave shape distortion; that is, the external circuit including the energizing source can have a very high impedance without causing the voltage wave across terminals 18 and I! to become distorted, or it can have a low impedance and still supply a substantially sinusoidal current.

The circuit of Figure 3 probably has a wider neld of application when the saturable inductance is made to produce the third harmonic, and does not have a unidirectional bias. In this case, the relationship between applied voltage and the current supplied to the circuit can be expressed by an equation substantiailly of the form:

Ir=B1E+BJE where Is is the magnitude of the fundamental current supplied and E is the magnitude of the sinusoidal applied voltage. In this equation, the constant Bi depends not only on the characteristics of the non-linear inductance, but also on the value of the capacitor 25, and in fact, B]. may be negative with B: being positive; negative values of current being capacitive and positive values inductive. In this case, the circuit becomes anti-rescnant when BiE is equal in magnitude to 33151 The circuit of Figure 8 as shown may be used in a wide variety of circuit arrangements, or an equivalent circuit may be used to obtain similar results. All that is necessary is that there be substantially in shunt relationship with my nonlinear inductance a low impedance path for current whose frequency is that of the harmonic generated in the saturable inductance. This low impedance path may include the energizing source or perhaps even a load, as long as the total impedance, excluding the non-linear in" ductance, is low at the frequency of the harmonic generated by the non-linear inductance.

Although Figure 3 shows the by-pass circuit applied to an inductance of the type shown in Figure 2 it can also be applied to a combination of the type shown in Figure l.

The description of my invention and the equations used apply in the strictest sense only to ideal cores without hysteresis or eddy current losses, but I have found that the results described can be substantially obtained when using com mon transformer iron of a good grade.

Although I have described, my invention with a certain degree of particularity, it is understood that the present disclosure has been made only by way of example, and that numerous changes in the details of construction on the combinations and arrangements of parts may be resorted to without departing from the spirit and scope of the invention as hereinafter claimed.

I claim as my invention:

1. A non-linear inductance having a plural ity of magnetic flux paths which saturate under different magnetizing forces, the total flux being related to the magnetizing current by an equation substantially of the form i-Ai+Aa= where, i, is the instantaneous value of the exciting current, the total flux, and A1 and A; are constants depending upon the physical and electrical properties of the inductance.

2. A non-linear inductance having a plurality of magnetic flux path which saturate under different magnetizing forces, the total flux being related to the magnetizing current by an equation substantially of the form i=-Ai+Az for positive values of where i is the instantaneous value of the exciting current, the total flux, and A1 and A: are constants depending upon the physical and electrical properties of the inductance.

3. In combination, a plurality of saturable magnetic flux paths, winding means associated with each of said paths, and circuit means interconnecting said winding means fcrming a two terminal combination, said two terminal combination having an alternate current characteristic substantially of the form Ir-BiI+B:P, E being the magnitude of an applied substantially sinusoidal voltage, I! being the magnitude of the fundamental current and Bi and Ba are constants depending upon the physical and electrical proportions of the inductance.

4. In combination, non-linear inductive means characterised by a relationship between sinusoidal applied voltage and fundamental current magnitude substantially of the form IF BlE+BJE and circuit means providing substantiaDy a short-circuit for third harmonic voltages across said non-linear inductive means,

where Bi and B: are constants depending upon the physical and electrical proportions of the inductance.

5. In combination, a non-linear inductance having a current-flux relationship substantially of the form Al+m where i is the exciting current, e the total flux, and A1 and A: are constants depending upon the physical and electrical proportions of the inductance, circuit means adapted to connect said inductance with an alternating current source of a specified frequency, and tuned circuit means connected with said non-linear inductance providing a low-impedance path to effectively short-circuit voltage of a frequency three times said specified frequency appearing across said non-linear inductance.

6. In combination, a non-linear inductance having a current-flux relationship substantially of the form i-Ai+As' for positive values of where i is the exciting current, the total flux, and A: and A: are constants depending upon the physical and electrical proportions of the inductance, biasing means for preventing flux reversals, circuit means adapted to connect said inductance with an alternating current source of a specified frequency, and tuned circuit means connected with said non-linear inductance providing a low-impedance path to eflectively shortcircuit voltage of a frequency twice said specified frequency appearing across said non-linear inductance.

7. An inductive element having a plurality of saturable magnetic flux paths excited by a common winding means, said flux paths being adapted to saturate under differing magnetomotive forces, the exciting current in said winding means and the total flux in said flux paths being related substantially by a cubic equation of the form e-Cd-Cfl where t is the exciting current, o the total flux, and C1 and C: are constants depending upon the physical and electrical proportions of the inductive element.

8. An inductive element having a plurality of saturable magnetic flux paths excited by a common winding means, said flux paths being adapted to saturate under differing magneto-motive forces. the exciting current in said winding means andthetotalfiuxinsaidfluxpaths beingrelated substantially by a quadratic equation of the form =Cii-Czi* for positive values of current, where i is the exciting current, e the total flux, and Ci and C: are constants depending upon the physical and electrical proportions of the inductive element.

9. In combination, an inductance having a magnetic core comprising a plurality of parallel flux paths, each of said flux paths being adapted to become saturated under a different magnetising force to produce a relationship between sinusoidal applied voltage and fundamental current magnitude substantially of the form circuit means for supplyingan alternating voltage of a specified frequency to said inductance, and resonant means for providing a low impedance path to a voltage of the third harmonic of said specified frequency generated by said inductance. h

10. In combination, an inductance having a magnetic core comprising a plurality of parallel flux paths, each of said flux paths being adapted to become saturated under a different magnetizing' force, circuit means for supplying an alternating voltage of a specified frequency to said inductance, biasing rneans'for preventing flux reversals in said flux paths, and resonant means for providing a low impedance path to a voltage of the second harmonic of said specified frequency generated by said inductance.

11. In combination, a non-linear inductance having a current-flux relationship substantially of the form i-A1-{-A3 where i is the exciting current. the total flux, and A1 and A3 are con-- stants depending upon the physical and electrical proportions of the inductance, circuit means adapted to connect said inductance with an alternating current source of a specified frequency, and tuned circuit means connected with said nonlinear inductance providing a low-impedance path to effectively short-circuit voltage of a frequency three times said specified frequency appearing across said non-linear inductance, said tuned circuit means in combination with said non-linear inductance forming a parallel ferro-resonant circuit with respect to said alternating current source.

12. In combination, a non-linear inductance having a current-flux relationship substantially of the form i=A1+A2 for positive values of where i is the exciting current, the total flux, and A1 and A2 are constants depending upon the physical and electrical proportions of the inductance, biasing means for preventing flux reversals, circuit means adapted to connect said inductance with an alternating current source of a specified frequency, and tuned circuit means connected with said non-linear inductance providing a low-impedance path to effectively short-circuit voltage of a frequency twice said specified frequency appearing across said non-linear inductance, said tuned circuit means in combination with said non-linear inductance forming a parallel ferro-resonant circuit. with respect to said alternating current source.

13. A non-linear inductance having a plurality of magnetic flux paths which saturate under different magnetizing forces, the total flux being related to the magnetizing current by an equation substantiallly of the form i=Ai+As where i is the the instantaneous value of the exciting current, the total flux, the A1 and A3 are constants depending upon the physical and electrical proportions of the inductance, the flux paths being constructed to make the first power term in said equation small in comparison with the third power term over most of the operating range.

14. A non-linear inductance having a plurality of magnetic flux paths which saturate under different magnetizing forces, the forces flux being related to the magnetizing current by an equation substantially of the form i=Ai+Ai for positive values of where i is the instantaneous value of the exciting current, c the total flux, and A1 and A: are constants depending upon the physical and electrical proportions of the inductance, the flux paths being constructed to make the first power term in said equation small in comparison with the second power term over most of the operating range.

15. Non-linear impedance means having a plurality of saturable magnetic flux paths of different characteristics and winding means for magnetizing the said magnetic flux paths, the magnetic fiux paths in cooperation with the winding means establishing a reactance which, when energized with a sinusoidal voltage, admits the fiow of current of the fundamental frequency and of only one harmonic frequency with the currents of the other harmonic frequencies substantially eliminated, the magnetic flux paths saturating at different portions of the sinusoidal voltage cycle and generating substantially equal and opposite voltages of the said other harmonic frequencies to substantially eliminate the flow of current of said other harmonic frequencies.

16. Non-linear impedance means having a plurality of saturable magnetic flux paths of different characteristics and winding means for magnetizing the said magnetic flux paths, the magnetic flux paths in cooperation with the winding means establishing a reactance which, when energized with a sinusoidal voltage, admits the flow of current of the fundamental frequency and of the third harmonic frequency with the currents of the other harmonic frequencies substantially eliminated, the magnetic flux paths saturating at different portions of the sinusoidal voltage cycle and generating substantially equal and opposite voltage of the said other harmonic frequencies to substantially eliminate the fiow of current of said other harmonic frequencies.

17. Non-linear impedance means having a plurality of saturable magnetic flux paths of different characteristics, winding means for magnetizing the said magnetic flux paths, and means for establishing a unidirectional biasing fiux in the magnetic flux paths, the magnetic flux paths in cooperation with the winding means establishing a rectance which, when energized with a sinusoidal voltage, admits the flow of current of the fundamental frequency and of the second harmonic frequency with the currents of the other harmonic frequencies substantially eliminated, the magnetic flux paths saturating at different portions of the sinusoidal voltage cycle and generating substantially equal and opposite voltages of the said other harmonic frequencies to substantially eliminate the flow of current of said other harmonic frequencies.

18. Non-linear impedance means having a plurality of saturable magnetic flux paths of different characteristics and winding means for magnetizing the said magnetic flux paths, the magnetic flux paths in cooperation with the winding means establishing a reactance which,

' when energized with a sinusoidal current, produces a voltage of the fundamental frequency and of only one harmonic frequency with the voltages of the other harmonic frequencies substantially eliminated, the magnetic flux paths saturating at different portions of the sinusoidal current cycle and generating substantially equal and opposite voltages of the said other harmonic frequencies.

19. Non-linear impedance means having a plurality of saturable magnetic flux paths of diiferent characteristics and winding means for magnetizing the said magnetic flux paths, the magnetic flux paths in cooperation with the winding means establishing a reactance which,

when energized with a sinusoidal current, produces voltage of the fundamental frequency and of the third harmonic frequency with the voltages of the other harmonic frequencies substantially eliminated, the magnetic flux paths saturating at different portions of the sinusoidal current cycle and generating substantially equal and opposite voltages of the said other harmonic frequencies.

20. Non-linear impedance means having a plurality of saturable magnetic flux paths of diiferent characteristics, winding means for 

